Why is granite cool to the touch and wood cabinets are not though they are in the same room at the same temperature and is the granite countertop really cooler?

Answer:

If the temperature of a room has remained constant for some time, all the objects in it should be at the same temperature. A granite countertop and a wooden cabinet door will be at the same temperature, but each has a different heat capacity. We need to look at that.

Let's say we have a block of granite and a block of wood the same size, and both are at the same temperature. Granite has a bit of variation in its density, but not as much as wood, so let's use oak, which is moderately dense as regards woods. The two blocks, though they are at the same temperature, have different amounts of thermal energy, or heat, in them, with the granite having more. Granite has more "material" in it than wood does, more atoms and molecules, and each one of them is a thermal storage unit with a given capacity. Granite, because it has more storage units, will require more energy to heat it up to another temperature than the wood would to heat it to the same temperature. The granite will also have to give up more energy to lower its temperature than wood would to drop to the same temperature. This is heat capacity.

Because granite has a higher heat capacity, it will sink more heat from the hand of an individual than the wood would. The granite has more places for the heat to go to, more of those "heat storage units" than the wood. This means that the granite will "suck heat" out of an individual's hand "better" than wood could. And this makes the granite feel cooler than the wood, even though they are at the same temperature.

Note that we didn't try to factor in the rate of heat transfer through the granite or the wood, but just looked at a "surface effect" here. But it is a perfectly good vehicle to explain the observations made in touching the countertop and the cabinet and noting the difference in the "coolness" of each material.